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Symplectic vector space
About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.
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TL;DR: In this article, the authors considered a discrete symplectic eigenvalue problem with separated boundary conditions and obtained formulas for the number of eigenvalues on a given interval of the variation of the spectral parameter.
Abstract: In this paper we consider a discrete symplectic eigenvalue problem with separated boundary conditions and obtain formulas for the number of eigenvalues on a given interval of the variation of the spectral parameter. In addition, we compare the spectra of two symplectic eigenvalue problems with different separated boundary conditions.
8 citations
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TL;DR: In this article, an infinite dimensional generalization of metaplectic representations (Weil representations) for the (double covering of) symplectic group is considered, where projective unitary representations of the infinite dimensional group are constructed via unitary implementors of Bogoliubov automorphisms.
8 citations
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TL;DR: In this paper, the product by generators of two nilpotent Lie algebras is introduced as a central extension of the direct sum and a procedure to construct symplectic forms in natural manner on quotient Lie algesbras of certain products by generators is presented.
Abstract: We introduce the product by generators of two nilpotent Lie algebras as a central extension of the direct sum and analyze symplectic structures on them. We show that, up to few exceptions, these products do not admit symplectic forms. Besides a general criterion, we indicate a procedure to construct symplectic forms in natural manner on quotient Lie algebras of certain products by generators.
8 citations
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TL;DR: In this article, the determinant identities of irreducible characters for the universal orthogonal and universal Schur functions using vertex operators were studied and expanded, and a new proof of the duality between the universal and universal functions using the vertex operator was given.
Abstract: Vertex operator realizations of symplectic and orthogonal Schur functions are studied and expanded. New proofs of determinant identities of irreducible characters for the symplectic and orthogonal groups are given. We also give a new proof of the duality between the universal orthogonal and symplectic Schur functions using vertex operators.
8 citations
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TL;DR: A variational principle introduced to select some symplectic connections lead- s to Þeld equations which, in the case of the Levi Civita connection of Kahler manifolds, are equivalent to the condition that the Ricci tensor is parallel.
Abstract: A variational principle introduced to select some symplectic connections lead- s to Þeld equations which, in the case of the Levi Civita connection of Kahler manifolds, are equivalent to the condition that the Ricci tensor is parallel. This condition, which is stronger than the Þeld equations, is studied in a purely sym- plectic framework. 1. A symplectic connection r on a symplectic manifold (M;!) of dimension 2n is a torsion free linear connection such that r! = 0. It is a standard fact (5) that the space E of symplectic connections on (M;!) is isomorphic (in a non-canonical way) to the space of completely symmetric, covariant, 3 tensor Þelds on (M;!). We have introduced in (3) a variational principle in order to single out particular symplectic connections, which we called preferred. The Lagrangian density is the "square" of the curvature tensor R of r and the scalar product on the space of curvature tensors is induced by !; it is not positive deÞnite. The functional on E has the form
8 citations